Clearing up a debate. Can you cancel these (X-49), (49-X) when X=49?

[compact burrow]

If canceled the answer ends up as 14. If not it becomes undefined because the denominator is 0.

[sterile elk]

Hello. When you work with limits, you should simplify the fraction first. Don't confuse that with cancelling 0/0, which is wrong. For example in this limit, as x approaches 49, x-49 approaches 0, but it's not strictly 0

Still, the second image is incorrect

(49-x)/(x-49) ≠ 1

[compact burrow]

But wouldn’t x-49 and 49-x still be equals regardless of what the limit is? Or do I have to transpose x before cancelling? Or could I not cancel it regardless?

And where is the wrong in the second image? Is it the cancel?

[sterile elk]

Yes, that's why you should cancel them and everything else you can before substituting x=49. Otherwise you get 0(14)/0

Also x-49 and 49-x are not the same

And that's also why the second image is wrong too

For example, yo don't cancel 3 with -3 and say 3/-3 = 1

That's not correct

[compact burrow]

Thx man. Get it now.

.close

[royal summit]

Solved

Post marked as solved by @compact burrow.

Use .unsolved if this was a mistake.

[compact burrow]

.unsolved

[royal summit]

Unsolved

Post marked as unsolved by @compact burrow.

Use .solved to mark as solved.

[compact burrow]

Wait. Is this right then?

Factorial method by a classmate

Part of my solutions for rationalization. Same answer.

[sterile elk]

Here isn't it (√x + 7) ?

What's the original question

[compact burrow]

49-X/√x-7 lim x->49 but our prof said no more tables so we could treat it more like substitution x=49

[sterile elk]

Ok in that case

[sterile elk]

This is correct

[sterile elk]

This is wrong because you get √x **+**7, not **-**7

[compact burrow]

Oh I forgot to change the signs lol. Is that the only thing wrong with it?

[sterile elk]

Yes

👍🏽

[compact burrow]

Thx

Very very thank you

.close